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Expansive dynamics on zero-dimensional groups

Published online by Cambridge University Press:  19 September 2008

Bruce P. Kitchens
Bruce P. Kitchens
Affiliation:
IBM T. J. Watson Research Center, Mathematical Sciences Department, P.O. Box 218, Yorktown Heights, NY 10598, USA
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Abstract

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If X is a compact, zero-dimensional group and T is an expansive, transitive automorphism then (X, T) is shown to be topologically conjugate to a full shift on finitely many symbols.

The problem of classifying such automorphisms up to simultaneous algebraic isomorphism and topological conjugacy is discussed but not solved. It is proved that for any entropy there are only finitely many such equivalence classes. When the entropy is log p for a prime p, there is only one equivalence class. All are then equivalent to

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 2 , June 1987 , pp. 249 - 261
Copyright
Copyright © Cambridge University Press 1987

References

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